Mix the crushed cookies with melted butter. Press the mixture evenly into a 9x13-inch baking dish and chill in the refrigerator for 5 minutes.
Beat the softened cream cheese with the powdered sugar until fluffy and smooth. Add 1 cup of the whipped topping and mix to combine. Spread this mixture over the chilled cookie crust. Freeze for 10 minutes.
In a bowl, whisk the chocolate pudding mix with cold milk until the mixture thickens. Spread it evenly over the cream cheese layer and let it sit in the refrigerator for about 10 minutes.
Spread the remaining whipped topping over the pudding layer and sprinkle the extra Oreo crumbs on top for garnish.
Refrigerate the assembled lasagna for at least 4 hours before serving. For cleaner slices, you can freeze it for 30 minutes prior to cutting.